Explicit bi-Hamiltonian construction yields canonical separating coordinates and momenta for the generalized Kaup-Kupershmidt system, with the same scheme applied to KdV5 and Sawada-Kotera cases.
The Hénon-Heiles System Revisited, Physica D: Nonlinear Phenomena 52 (1991), 204–210
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Canonical separating coordinates in the generalized cubic H\'enon-Heiles systems
Explicit bi-Hamiltonian construction yields canonical separating coordinates and momenta for the generalized Kaup-Kupershmidt system, with the same scheme applied to KdV5 and Sawada-Kotera cases.